The Ivory Coast international posted screenshots on Instagram of racist abuse he had received by direct messages following the Premier League match that saw City defender Aymeric Laporte sent off for a foul on the forward.
City are now five points behind Premier League leaders Chelsea and face Manchester United in a derby at Old Trafford next weekend.
Premier League: Manchester City manager Pep Guardiola praises league's quality ahead of Chelsea match
The champions travel to Chelsea on Saturday three points behind the Blues, Liverpool and Manchester United at the top of the table.
Premier League: Jack Grealish bags first Manchester City goal as champs cruise; Liverpool beat Burnley
But Grealish's first goal since January helped show Pep Guardiola's side they can cope without Harry Kane if their prolonged pursuit of the Tottenham striker ends in failure.
A familiar foe stands in his way at Wembley, but win or lose, Luis Enrique will do it his own way.
After two tension-filled draws against Sweden and Poland, Spain were left scrambling to qualify, with Luis Enrique admitting he would have taken any position in the group as long as it meant going through.
Euro 2020: Spain, Portugal play out goalless draw in front of nearly 15,000 fans in pre-tournament friendly
Cristiano Ronaldo had a frustrating night on his first game in Madrid since leaving Real in 2018 and came close to scoring twice and set up a good chance Diogo Jota failed to take advantage of.
Euro 2020: Veteran defender Sergio Ramos left out as Spain include France-born Aymeric Laporte in 24-man squad
The absence of veteran defender Ramos means there is not a single Madrid player in the Spain squad.
Laporte could be a valuable addition to the Spanish squad given the central defence has been a problem area for coach Luis Enrique.
Fernandinho says Manchester City will 'do everything' to win Champions League after clinching league title
Pep Guardiola's men have wrapped up the Premier League with three games to spare after also winning the League Cup in April.
The Spanish Council of Ministers has granted Spanish nationality to Laporte, who was born in Agen, France but never played for the French senior team, despite three call-ups to the squad between 2016 and 2020.
Aymeric Laporte's header eight minutes from time finally ended Tottenham's resistance as their 13-year wait to win a trophy goes on.
Premier League: Manchester City defender John Stones hails Ruben Dias' impact in his first season at club
Stones has started 15 times with Ruben Dias this season, with City conceding just two goals during these instances, and the England international feels it comes down to the work on the training ground, irrespective of whom he teams up with.
Stones, who scored two of the four goals against Palace, has been outstanding in City's recent run of form.
Premier League: Diogo Jota inspires Liverpool's comeback win over Sheffield United; Manchester United, Chelsea share points
Jurgen Klopp's champions, without injured defensive talisman Virgil van Dijk, are now unbeaten in 62 Premier League home games at Anfield but had to dig deep after falling behind to an early penalty scored by Sander Berge.
City, who have won the League Cup for the past three seasons, start the defence of their trophy against Bournemouth on Thursday and Guardiola knows they cannot afford to lose more players.
Premier League: Midfielder Ilkay Gundogan becomes latest Manchester City player to test positive for COVID-19
Gundogan is the third City player to return a positive test this month, following Aymeric Laporte and Riyad Mahrez.
All players or club staff who have tested positive will self-isolate for a period of 10 days.
A video posted on social media in Iceland showed Foden and Greenwood meeting women from outside the team bubble. Reports said they had brought them back to England's team hotel, but the manager said that was not the case.
Manchester City said both Riyad Mahrez and Aymeric Laporte have not displayed any symptoms and are in self-isolation.